Download AP/ACC-Statistics Course Outline Chaminade College Preparatory

AP/ACC-Statistics Course Outline
Chaminade College Preparatory School course: AP/ACC-Statistics (STA 470)
Advanced Credit Program through the University of Missouri – St. Louis course: MATH 1310
Elementary Statistical Methods
Course Outline:
UNIT I: EXPLORING AND UNDERSTANDING DATA (15 BLOCKS)
Section A
Data (Chapter 2)
3 Blocks
Who, what, when, where, why (and sometimes how).
Section B
Categorical and quantitative variables
Quiz
Displaying and Describing Categorical Data (Chapter 3)
3 Blocks
Frequency and relative frequency tables
The area principle
Bar charts, pie charts
Computer output: keys to observe in bar charts and pie charts generated by
computer packages
Contingency tables and conditional distributions
Section C
Simpson’s paradox
Quiz
Displaying and Summarizing Quantitative Data (Chapter 4)
3 Blocks
Histograms, relative frequency histograms, stem-and-leaf displays, and dotplots
Interpreting quantitative data: communicating the shape, center, and spread of
the distribution
Quartiles, IQR, and outliers
5-number summary, mean, variance, and standard deviation
Calculator application: Inputting a list of values, draw histograms, calculate 5number summary, mean, and standard deviation
Quiz
Computer output: keys to observe in displaying and summarizing quantitative
variables by computer packages
Section D
Understanding and Comparing Distributions (Chapter 5)
2 Blocks
Boxplots, 5-number summaries, and outliers
Interpreting distributions of groups by comparing groups with histograms and
boxplots
Calculator application: Draw histograms and boxplots , aid in determining outliers
Quiz
Computer output: comparing distributions generated by computer packages
Section E
The Standard Deviation as a Ruler and the Normal Model
Standardizing of values, z-scores, and normal distribution
4 Blocks
Shifting and rescaling data
68-95-99.7 Rule
Normal percentiles and area under the curve
Using z-tables, and calculator statistics functions
Assessing normality and normal probability plots
Calculator application: z-score to area under the curve, area less than a value back
to a z-score, and drawing normal probability plots
Interpreting the difference between raw score, standardized score, area under
the curve, and percent of coverage of under the curve
Unit I Test
UNIT II: EXPLORING RELATIONSHIPS BETWEEN VARIABLES (5 BLOCKS)
Section A
Scatterplots, Associations, and Correlation
2 Blocks
Scatterplots (describing pattern, form, direction, strength, and outliers)
Response and explanatory variables
Correlation
Section B
Calculator application: Drawing scatterplots, and computation of means and
correlation of variables
Quiz
Linear Regression
3 Blocks
The least squares regression line
Predicted values and residuals
Correlation, standard deviation, and regression slope
Means of x and y, and regression intercept
Interpreting the value 𝑅2 - the variation accounted for by the explanatory
variable
Calculator application: interpretation of least square regression line, and the
explanation of the variation of the response variable by the explanatory variable
Unit II Test
Computer output: keys to interpretation of regression table of results made by
statistical packages
UNIT III: GATHERING DATA (4 BLOCKS)
Section A
Understanding Randomness
2 Blocks
Simulations
Random numbers
Calculator application: Use of lists, random integer generators, and data displays
Project: emphasis on developing the components, objectives, and analysis of a
simulation. Class divided into groups, each taking either “The Spread of a Rumor”,
“The Duck Hunters”, “Airline Overbooking”, or “The Spread of an Epidemic” project.
Students will:
(a) develop the individual component to be randomly generated
(b) define the trial to be simulated by the components
Quiz
(c) define the response variable to be recorded
(d) perform an analysis of multiple trials
(e) interpret the results in order to present any conclusions that can be drawn from
the simulation.
Section B
Sample Surveys
2 Blocks
Examine a part of the whole, bias
Randomize
Sample size, census, population, parameters, statistics
Simple random samples (SRS)
Unit III Test
UNIT IV: RANDOMNESS AND PROBABILITY (8 BLOCKS)
Section A
From Randomness to Probability
3 Blocks
Trials, outcomes, events, and sample spaces
Law of large numbers
Modeling probability, personal probability, and formal probability
Complement rule, addition rule, and multiplication rule
Fundamental theorem of statistics
Assumptions and conditions
Sampling distribution model for the mean
Section B
Mean and standard deviation
Quiz
Probability Rules!
2 Blocks
The General Addition Rule
Conditional Probability from a contingency table
The General Multiplication Rule
Independence
Drawing without Replacement
Section C
Tree Diagrams
Quiz
Random Variables
1 Block
Interpreting the expected value as an estimate of the center of a probability
distribution
Section D
Interpreting the variance as an estimate of the spread of a probability distribution
Quiz
Probability Models
2 Blocks
Geometric probability model for Bernoulli Trials
Independence
Binomial probability model for Bernoulli Trials
Identifying the model used for a particular situation
Normal Model used to approximate a binomial model
Unit IV Test
Calculator application: Factorials, combinations, geometric distribution, binomial
distribution, and approximations using Normal distribution
UNIT V: CONFIDENCE INTERVALS AND HYPOTHESIS TESTING (7 BLOCKS)
Section A
Confidence Intervals for Proportions
2 Blocks
Observed proportion and standard error
Meaning of confidence intervals
One-proportion z-interval
Margin of error, critical values
Assumptions and conditions necessary for interpreting confidence interval
Choosing sample size
Calculator application: Calculation of one-proportion z-interval
Section B
Testing Hypotheses About Proportions
Quiz
1 Block
Hypotheses
Standard deviation and standard error
P-value and hypothesis testing
Two-sided and one-sided hypothesis
Section C
Calculator application: One and Two-sided hypothesis testing using one-proportion
z-test
Quiz
Tests, Errors, and the Power of the Test
2 Blocks
Null hypothesis
Alpha levels, statistical significance
Confidence intervals and hypothesis tests
Type I and Type II errors
Power
Selecting the alternative hypothesis to reduce the Type I and Type II errors
Calculator application: One-sample z-interval and one-sample z-test
Quiz
Project: using Minitab to conduct an inference study on one sample from a
population with known standard deviation
Section D
Comparing Two Proportions
2 Blocks
Variance of sum/difference of random variables
Standard deviation of the difference between two proportions
Assumptions and conditions necessary for interpreting the difference between
two proportion
Sampling distribution for two proportions
Two-proportion z-interval
Standard error of the difference
Pooled two-proportion z-test
Unit V Test
Calculator application: Two-proportion z-interval, two-proportion z-test, and the
concept of pooling
FIRST SEMESTER EXAM
UNIT VI: LEARNING ABOUT THE WORLD (12 BLOCKS)
Section A
Inference About Means
3 Blocks
Central limit theorem
Standard deviation of the mean
Gosset’s t-model
Confidence interval for the mean, one-sample t-interval
Assumptions and conditions necessary for t-model being used
Standard error of the mean, degrees of freedom
One-sample t-test
Margin of error, and sample size
Calculator application: One-sample t-interval and one-sample t-test
Quiz
Project: Minitab project based on illustrating the Central Limit Theorem,
emphasizing comparisons of descriptive statistics, means, and medians.
Section B
Comparing Means
3 Blocks
Standard deviation of the difference of means
Standard error of the difference of means
Two-sample t-interval
Degrees of freedom formula
Assumptions and conditions necessary for two-sample t-model being used
Alternative degrees of freedom
Pooled t-test
𝑠𝑝𝑜𝑜𝑙𝑒𝑑
Standard error for pooled difference of means
Confidence interval for pooled difference of means
Hypothesis testing for pooled difference of means
Calculator application: Two-sample t-interval, pooled t-test, and the aggression
computation of the degrees of freedom, confidence interval /hypothesis test with
pooled difference of means
Quiz
Computer output: study the method of displaying the results of a two-sample
method in a statistical package
Section C
Paired Samples and Blocks
Paired data, blocking, and matching
Paired t-test
Assumptions and conditions
2 Blocks
Confidence intervals for matched pairs
Effect size and blocking
Section D
Computer output: interpretation of different statistical packages display of a
matched pairs and paired t analyses
Quiz
Comparing Counts
1 Block
Goodness-of-Fit
Assumptions and conditions
Chi-square calculations
Chi-square test of homogeneity
Assumptions and conditions
Examining the residuals
Section E
Calculator application: Chi-square goodness of fit testing, and Chi-square test of
homogeneity
Quiz
Inference for Regressions
3 Blocks
Population and sample, parameters and statistics
Idealized line and fitted line
Assumptions and conditions
Residuals
Spread around the line, spread of the x’s, and sample size
Standard error for the slope
Sampling distribution for regression slopes
Hypothesis tests and confidence intervals
Confidence interval for the predicted mean value of 𝑥𝑦
Prediction interval for an individual with that x-value
Calculator application: hypothesis testing for slope and regression, and confidence
intervals for predicted mean and individual x-value
Unit VI Test
Computer output: statistical summary and regression analysis output from
different statistical package
UNIT VII: REVISITING EARLIER TOPICS (20 BLOCKS, GROUP-FOCUSED INSTRUCTION)
Section A
Re-expressing to equalize spread across groups
1 Block
Alleviating the problem of comparing groups by transforming data using different
mathematical functions
Section B
Section C
Normal Probability Plots
1 Block
Using the normal probability plot along with histograms to judge whether a
Normal Model may be appropriate
Quiz
Applications of Correlations and Scatterplots
1 Block
Correlation tables
Straightening scatterplots
Section D
Investigating Linear Regressions
2 Block
Residuals used to investigate patterns
Residual standard deviation
Regression assumptions and conditions necessary for appropriate predictions
Analyzing two regressions
Calculator application: Display of residual plots
Section E
Regression Wisdom
Test
2 Blocks
Regression analysis
Extrapolation
Outliers, leverage, and influence
Lurking variables and causation
Section F
Computer output: working with summary values generated from statistical
packages
Quiz
Re-expressing Data to Get the Regression Straight
2 Blocks
Goals of re-expression
Ladder of Power
Exponential, Logarithmic, and Power functions
Section G
Calculator application: Calculator short-cut regressions for Quadratic, Cubic,
Quartic, Natural Logarithmic, Exponential, Power, and Logistic regressions
Quiz
Sample Surveys
2 Blocks
Stratified random sampling
Cluster and multistage sampling
Systematic samples
Defining the actual population to clarify the variables to be studied
Section H
Valid surveys
Quiz
Experiments and Observational Studies
4 Blocks
Observational studies, prospective studies
Random assignment
Factors, response variables, levels, and treatments
Subjects (participants) and experimental units
Control, randomize, replicate, and block
Diagrams
Sample surveys vs. experiments
Control treatments, blinding, and placebos
Random block design
Matching
Confounding
Section I
Project: small group problem as students design and administrate a survey on a
topic of their choice. The students will collect and analyze data using descriptive
and inferential statistics, drawing conclusions from their analysis.
Test
Probability Rules
1 Block
Reversing the conditions of conditional probability
Section J
Bayes’s Rule
Quiz
Sampling Distribution Models
1 Block
Simulating the sampling distribution of a mean
Section K
Tests and Intervals
1 Block
A 95% confidence interval for small samples
Power
Reducing Type I and II errors
Section L
Section M
Computer output: examining different statistical packages representation of
hypothesis tests
Quiz
Comparing Two Proportions
1 Block
Null hypothesis means no difference
Quiz
Inferences About Means
1 Block
Background behind degrees of freedom
Computer output: investigate statistical packages examination of inference for
means
Test
Final exam will precede the AP test and will emphasize the format used on the AP exam. AP
material will be used to emphasize the topics in that context.